Finite Group Databasebeta

← #10823428

Subgroups — #10823428

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×#5026C211yesmaximal, characteristic, complemented
3C2×#5014C211yesmaximal, characteristic, complemented
4C4×#930C211yesmaximal, characteristic, complemented
5#71743C211yesmaximal, characteristic, complemented
6#71739C211yesmaximal, characteristic, complemented
7#71728C211yesmaximal, characteristic, complemented
8#71722C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#71694C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic
12#71679C211yesmaximal, characteristic, complemented
13#71631C211yesmaximal, characteristic, complemented
14#71609C211yesmaximal, characteristic, complemented
15#71529C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C3×#529—24no—
18C3×#529—24no—
19C2×C3×#126—21no—
20C2×C3×#125C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C22×C3×C42C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×C4×#67—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5213—21no—
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5026—24no—
46#5014—24no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4940—21no—
52#4939C2211yescharacteristic
53C4×(C2×D3)⋊C4—21no—
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529D311yescharacteristic, complemented
65C2×#442—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C3×#126—28no—
90C3×#125—22no—
91C3×#125—22no—
92C3×#124—22no—
93C3×#124—22no—
94C3×#123—28no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8D414yescomplemented
101C3×C4×D4—28no—
102C3×C4×D4—22no—
103C3×C4×D4D414yescomplemented
104C3×#117—28no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42—21no—
117C2×C3×C42—22no—
118C2×C3×C42—22no—
119C2×C3×C42D411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#215—22no—
125C2×#215—22no—
126C2×#215—22no—
127C2×#213—22no—
128C2×#213—22no—
129C2×#213—22no—
130#930—22no—
131#930—22no—
132C4×#67—44no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C4×D12—22no—
147C4×D12—22no—
148#835—22no—
149#835—22no—
150#835—22no—
151#832—22no—
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#830—22no—
158#830—22no—
159#809—22no—
160#809—22no—
161#808—22no—
162#807—22no—
163#803—22no—
164#803—22no—
165C22×SD16—31no—
166C22×D8—31no—
167#529—24no—
168#529—24no—
169C2×#126—21no—
170C2×#125C2×D311yescharacteristic
171C2×#124C2×D311yescharacteristic
172C2×#123—21no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4C2×D311yescharacteristic
181C2×#117—21no—
182C22×C42C2×D311yescharacteristic
183#442—64no—
184#440—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97—31no—
199#390—31no—
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—24no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4C2×D412yes—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—24no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—41no—
244C22×C3×C4—41no—
245C22×C3×C4—41no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2411yescharacteristic
254C2×#67—24no—
255C2×#67—42no—
256C2×#67—42no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12#4112yes—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4C2×D412yes—
276C3×C4⋊C4C2×D412yes—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C42—22no—
283C3×C42—22no—
284C3×C42—24no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42C2×D412yes—
288C3×C42C2×D412yes—
289#217—42no—
290#215—28no—
291#213—28no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3#4112yes—
302Dic3⋊C4—42no—
303C4×Dic3—42no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8#4112yes—
315C2×C3⋊C8#4112yes—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—21no—
322C23×C4—61no—
323C23×C4#6711yescharacteristic
324C23×C4#6711yescharacteristic
325C23×C4C22×D311yescharacteristic
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×D8—62no—
330C2×D8—62no—
331C2×D8—62no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—31no—
336#126—28no—
337#125—22no—
338#125—22no—
339#124—22no—
340#124—22no—
341#123—28no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344#121—22no—
345#121—22no—
346#121—62no—
347#121—62no—
348C4×Q8—22no—
349C4×Q8#6714yescomplemented
350C4×D4—28no—
351C4×D4—22no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—124no—
355C4×D4#6714yescomplemented
356#117—28no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—21no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—61no—
381C2×C42#6711yescharacteristic
382C2×C42#6711yescharacteristic
383C2×C42C22×D311yescharacteristic
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#97—62no—
398#97—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3AGL(1,ℤ/8)12yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—22no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—48no—
431C3×D4—41no—
432C3×D4—41no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—48no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4#12012yes—
463C2×C3×C4#12012yes—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470#67—48no—
471C2×Dic3—22no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480D12—22no—
481D12—22no—
482D12—41no—
483D12—41no—
484C4×D3—84no—
485C3⋊C8—22no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C3⋊C8—41no—
489C24—21no—
490C24—61no—
491C24C2×#6711yescharacteristic
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×#6712yes—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—32no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—64no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4C2×#6712yes—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4C2×#6711yescharacteristic
541C22×C4C2×#6711yescharacteristic
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—68no—
547D8—68no—
548C2×C8—32no—
549C2×C8—32no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—32no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—122no—
573C4⋊C4C2×#6712yes—
574C4⋊C4C2×#6712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—22no—
586C42—22no—
587C42—24no—
588C42—21no—
589C42—21no—
590C42—122no—
591C42C2×#6712yes—
592C42C2×#6712yes—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57511yescharacteristic
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—42no—
627C3×C4—41no—
628C3×C4—42no—
629C3×C4#52511yescharacteristic
630C3×C4#52511yescharacteristic
631C3×C4#53211yescharacteristic
632C3×C4#53211yescharacteristic
633Dic3—42no—
634Dic3—81no—
635Dic3—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—62no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23#94912yes—
657C23C22×#6711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—62no—
668D4—62no—
669D4—128no—
670D4—121no—
671D4—121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—62no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—244no—
711C2×C4#95312yes—
712C2×C4#95312yes—
713C2×C4D3×#4111yescharacteristic
714C2×C4D3×#4111yescharacteristic
715C2×C4D3×#4111yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4C22×#6711yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—62no—
720C8—62no—
721C8—121no—
722C8—121no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3#238811yescharacteristic
726C2×C3#300511yescharacteristic
727C2×C3#300611yescharacteristic
728C2×C3#311111yescharacteristic
729C2×C3#311411yescharacteristic
730C2×C3#318011yescharacteristic
731C2×C3#318311yescharacteristic
732D3—82no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22C2×#94911yescharacteristic
755C22#582211yescharacteristic
756C22#582211yescharacteristic
757C22#582211yescharacteristic
758C22#582811yescharacteristic
759C22#583211yescharacteristic
760C22C2×#95311yescharacteristic
761C4—22no—
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4#582811yescharacteristic
773C4#582811yescharacteristic
774C4#583211yescharacteristic
775C4#583211yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—42no—
778C2—82no—
779C2—242no—
780C2#8313711yescharacteristic
781C2#8313911yescharacteristic
782C2#8314211yescharacteristic
783C2#8314311yescharacteristic
784C2#8408111yescharacteristic
785C2#8408211yescharacteristic
786C2#8409511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#529C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenterC2×#529D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×#5026C2semidirect
3. C2×#5014C2semidirect
4. C4×#930C2semidirect
5. #71743C2semidirect
6. #71739C2semidirect
7. #71728C2semidirect
8. #71722C2semidirect
9. #71699C2semidirect
10. #71694C2semidirect
12. #71679C2semidirect
13. #71631C2semidirect
14. #71609C2semidirect
15. #71529C2semidirect
64. C2×#529D3semidirect
100. C3×C4×Q8D4semidirect
103. C3×C4×D4D4semidirect
349. C4×Q8#67semidirect
355. C4×D4#67semidirect
776. C3#23575semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#5292
C2×#50262
C2×#50142
C4×#9302
#717432
#717392
#717282
#717222
#716992
#716942
#716842
#716792
#716312
#716092
#715292
#235753